There were 242 red, green and white pens in a box. 2 white pens were removed from the box and the ratio of the number of red pens to the number of green pens to the number of white pens became 5 : 2 : 9. Then some grey pens were added and the ratio of the number of white pens to the number of grey pens was 9 : 9.

1. What was the ratio of the number of red pens to the number of green pens to the number of white pens at first?
2. How many pens were in the box in the end?

	Red	Green	White	Grey	Total
Before	5 u	2 u	9 u + 2	0	242
Change 1	No change	No change	- 2		- 2
After 1	5 u	2 u	9 u		240
Change 2	No change	No change	No change	+ 9 u
After 2	5 u	2 u	9 u	9 u

(a)
Total number of pens at first
= 5 u + 2 u + 9 u + 2
= 16 u + 2

16 u + 2 = 242
16 u = 242 - 2
16 u = 240

1 u = 240 ÷ 16 = 15

Number of red pens at first
= 5 u
= 5 x 15
= 75

Number of green pens at first
= 2 u
= 2 x 15
= 30

Number of white pens at first
= 9 u + 2
= 9 x 15 + 2
= 137 

At first
Red pens : Green pens : White pens
75 : 30 : 137

(b)
Total number of pens in the box in the end
= 5 u + 2 u + 9 u + 9 u
= 25 u
= 375

Answer(s): (a) 75 : 30 : 137; (b) 375